Thursday, October 28, 2010

Who Can Finish Unbeaten – The Odds

Yesterday I posted that Oregon had a 22.6% chance of finishing the season without a loss, using a mathematical model based on Sagarin’s Predictor and the percentages of wins based on Vegas spreads.

When you think about it, the odds on Oregon aren’t at all far fetched. The Ducks have 5 games remaining. If you took an “average” team with a 50% chance of winning every game, their mathematical expectation of winning 5 in a row would be only 3.13% (0.50 to the 5th) Oregon, with better odds than 50-50 against most opponents, ends up with a 22.6% chance in this model, much higher than your average team might expect (though significantly lower than what the public might expect).

So what about the rest?

Using the same model, we get the following for the current undefeated teams (by BCS standings) –

Auburn 12.8%
Boise State 37.7%
TCU 59.7%
Michigan State 20.1%
Missouri 31.2%
Utah 11.5%

This does not include conference playoff games for Auburn or Missouri (don’t know their opponents), so their odds are even lower.

So it looks pretty grim for Auburn. Utah (who plays TCU) is also likely to lose.

Does this modeling bode well for Boise State, despite their probably lower than expected chance of around 38%?

Not necessarily. I believe that not only will all the major conference unbeatens have to lose for Boise to make the BCS title game, there are a couple of one loss teams that still might jump them. As for the chances that ALL the 4 major conference teams lose (Auburn, Michigan State, Oregon and Missouri) the odds are only 37.1%, despite all of them having a less than 25% chance of winning the table. Since there is about a 2 in 3 chance one of the four runs the table, in all likelihood at least one of the four wins out.

Moreover, if Boise is likely to not win out, maybe its TCU that will be making non-BCS waves at the end of this year.

This modeling has sparked a number of interesting ideas, including coming up with percentages of various team's chances of making the BCS title game.

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